Steve manages a skate park and he has been analyzing the attendance data. Steve finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 5x. Steve also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by g(x) = −x + 6. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.

1) The solution obtained from the graph is x = 1

2) An increase in temperature of one degree from the base temperature will lead to an equilibrium, where the number of people leaving the park equals the number of people visiting the park

Step-by-step explanation:

The equation of the two functions are;

f(x) = x⁵ and g(x) = -x + 6

The solution that satisfies the two functions is f(x) = g(x), which gives;

5ˣ = -x + 6

We note that, when x = 1, we have;

5¹ = 5 and  -(1) + 6 = 5

Therefore a solution is x = 1

The meaning of the solution is that for a temperature increase of one degree, the number of people visiting the park is equal to the number of people leaving the park.

$450

step-by-step explanation:

first, you have to multiply 150x2=300

next, you have to add 150+300= 450

substitute,

circle 1 = 5

circle 2 = 20

circle 3 = 44

in this case no matter how you add, you will always get a perfect square..

hence proved

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